Elliptic problems with rough boundary data in Nikolskii spaces - Murach, A.A.; Chepurukhina, I.S. (Reports of the National Academy of Sciences of Ukraine, 2021)
We investigate a general elliptic problem given in a bounded Euclidean domain with boundary data in Nikolskii spaces of low, specifically, negative order. The right-hand side of the elliptic differential equation is supposed to be an integrable function. We establish the Fredholm property of the problem, maximal regularity, and a priori estimate of its generalized solutions in the spaces indicated. We give an application of these results to some elliptic problems with boundary conditions induced by a Gaussian white noise